The present invention relates to a rear projection display and more particularly to a projection display which is capable of reducing radial two dimensional moire disturbance appearing in a screen constituted by three sheets of members or more.
Most of the prior art rear projection displays employ a screen constituted by two sheets of members. Of the two sheets of members, one of them is a Fresnel lens and the other is a longitudinal stripe-like lenticular lens for emitting horizontally rays.
In order to emit rays vertically as well, a screen constituted by three sheets of members should be used. However, there arises a problem that if the number of members constituting the screen is increased, the reflection loss of light is correspondingly increased (first problem). In addition, there arises another problem that in that case, the complicated moire disturbance will appear (second problem).
With respect to the first problem, i.e., the problem of the surface reflection loss, out of the above-mentioned problems, a measure of solving that first problem has followed the recent technical improvements. This measure is to apply an antireflection coating to a surface of the member constituting the screen. The application of the antireflection coating allows the matching with the refractive index of the member to be realized, and therefore, the reflection loss can be reduced.
However, of the above-mentioned problems, the second problem has been left unsettled. Further, the improvements in the recent computer technology have required a display which has the larger number of scanning lines. That is, in the present television broadcasts, as well known, the number of scanning lines per frame is about 500. However, along with the improvements in the computer technology, a display having the scanning lines of about 2,000 has been required. In order to realize such a display, it is necessary to use a screen having a picture element size, which is 1/4 times in length and breadth as small as the conventional one.
In U.S. Pat. No. 4,725,134 to Masanori Ogino, there is described the principle of appearance of the moire disturbance in a screen constituted by two sheets of members. More specifically, it is described that the moire disturbance appears due to interference with a Fresnel lens having a concentric circle structure and it appears remarkably in the right and left ends of the screen. As apparent from the description in U.S. Pat. No. 4,725,134, the moire disturbance becomes remarkable as the picture element size is smaller (in the case where a pitch of the Fresnel lens is fixed).
In U.S. Pat. No. 4,725,134, there is not described the principle of appearance of the radial moire disturbance appearing in the diagonal corners peculiar to a three-sheets screen, and the means of coping therewith. Therefore, the present invention was made in order to complement U.S. Pat. No. 4,725,134.
U.S. Pat. No. 4,725,134 was given to Masanori Ogino as the applicant for letters patent on Feb. 16, 1988, and all disclosure of which patent is incorporated herein by the reference.
FIG. 1 shows one example of the prior art transmissive screen. For the sake of simplifying the analysis, first, it is assumed that a projection light source is a point source. In the figure, the reference numeral 1 designates a Fresnel sheet; the reference numeral 1' designates a Fresnel lens, which is provided on a light emitting surface of the Fresnel sheet 1; the reference numeral 2 designates a stripe-like lenticular sheet for vertical divergence; the reference numeral 2', a transverse stripe-like lenticular lens provided on a light incident surface of the lenticular sheet 2; the reference numeral 3, a lenticular sheet for horizontal divergence; the reference numeral 3', a lenticular lens provided on a light incident surface of the lenticular sheet 3; the reference numeral 3", a lenticular lens provided a light emitting surface of the lenticular sheet 3. In this connection, a pitch (T.sub.0) of the Fresnel lens 1' is 0.1 mm, a pitch (T.sub.1) of the lenticular lens 2' is in the range of 0.5 to 0.6 mm, a pitch of the lens 3' is in the range of 0.5 to 0.6 mm, and a pitch (T.sub.2) of the lens 3" is in the range of 0.5 to 0.6 mm. Now, refer to U.S. Pat. No. 4,432,010 to Masanori Ogino for the details of a method of constructing the lenses 3' and 3". However, in U.S. Pat. No. 4,432,010, the moire disturbance 6 and 7 as shown in FIG. 2 is not mentioned.
All disclosure of U.S. Pat. No. 4,432,010 to Masanori Ogino: Application No. 308,590, filed on Oct. 5, 1981 is incorporated herein by the reference.
As the coordinate system for representing systematically the whole moire disturbance 5, 6 and 7, as shown in FIG. 2, both the rectangular coordinate system (x, y) and the polar coordinate system (R, .theta.) are employed.
FIG. 3 shows a cross sectional view of the Fresnel lens and a point source 8. In the figure, rays applied from the point source 8 to a screen is converted into parallel emitted rays by the Fresnel lens 1'. In this connection, as indicated by hatched line parts in the figure, light-absence parts appear periodically on the side of a light emitting surface of the Fresnel lens 1'. That is, the Fresnel pitch period component appears unavoidably in the luminance distribution.
The luminance distribution of the rays emitted from the Fresnel lens is, when performing the Fourier analysis, expressed by the following expression. ##EQU1## where d denotes the duty factor in the hatched line parts, i.e., the light-absence parts of the exit surface of the Fresnel lens in FIG. 3. A value of d takes zero in the central part of the screen and about 0.4 in the peripheral part of the screen. Therefore, an amplitude a.sub.0 of the fundamental wave component is zero in the central part of the screen and about 0.5 in the peripheral part of the screen.
Next, the function of the lenticular lens 2' will hereinbelow be described with reference to FIG. 4.
In general, the function of the lens is, when making parallel rays incident thereon, to convert the height coordinate of the incident light (position coordinate, i.e., y in FIG. 4; the origin thereof corresponds to the center of the surface of the lenticular lens 2' (or 14) as shown in FIG. 4) into the vertical direction .theta.(y) of the emitted light. Then, a lenticular lens designated by the reference numeral 14 will be described later. Therefore, the lenticular lens serves to convert periodically the height coordinate of the incident light into the vertical coordinate of the emitted light. Thus, if an observer for observing the screen located in the distance observes the screen from a certain specific direction, the observer will observe light which is periodically sampled with respect to the height direction by the lenticular lens.
The sampling structure T1(y) thereof is expressed mathematically as follows. ##EQU2##
In the same manner, the lenticular lens 3" in FIG. 1 serves to convert the transverse position coordinate of the incident light into the horizontal coordinate of the emitted light. Therefore, the sampling structure T.sub.2 (x) thereof is expressed mathematically as follows. ##EQU3##
In the above expression, the origin of the x-axis corresponds to the center of the lenticular lens 3'.
Therefore, the pattern T.sub.0,1,2 at which the observer looks on the screen surface is expressed quantitatively as follows. ##EQU4##
In the above expression, the low spatial frequency components are easy to be remarkable, and thus they are referred to as "the moire disturbance".